NUMERICAL STUDY ON NATURAL CONVECTION HEAT TRANSFER INSIDE RECTANGULAR ENCLOSURE FILLED WITH ANISOTROPIC POROUS MEDIA

Natural convection heat transfer inside horizontal rectangular enclosure filled with the anisotropic porous media, with isothermally heated bottom and cooled top while the vertical walls are adiabatic, is analyzed numerically by applying the Brinkman model-a modified form of Darcy model giving consideration to the viscous effect. The results show that: (1)the permeability ratio (K*=Ky/Kx) is an important factor affecting natural convection heat transfer in the porous media. As K' decreases, the circulation intensity of the natural convectioncells increase significantly, resulting in an enhancement of heat transfer coefficient; (2)the increase of Darcy number (aa=Ky/H2) implies that the viscous effect is more significant. As Da≥10-, there exists a certain difference between the Darcy model and the Brinkman model. It is more significant at a lower permeability ratio. In particalar, with K*≤0. 25, the Nusselt number for Da=10-3 would differ form that of Darcy model up to an amount of 30K. The Darcy flow as depicted by Darcy model is no longer existing and an analysis neglecting the viscous effect will inevitably be of considerable error.

MHD natural convection in porous media-filled enclosures

In this work, the magnetohydrodynamics （MHD） natural convection heat transfer problem inside a porous medium filled with inclined rectangular enclosures is investigated numerically. The boundary conditions selected on the enclosure are two adiabatic and two isothermal walls. The governing equations, continuity, and Forchheimer extension of the Darcy law and energy are transformed into dimensionless forms by using a set of suitable variables, and then solved by using a finite difference scheme. The governing parameters are the magnetic influence number, the Darcy Rayleigh number, the inclination angle, and the aspect ratio of the enclosure. It is found that the magnetic influence number and the inclination angle have pronounced effects on the fluid flow and heat transfer in porous media-filled enclosures.

Natural Convection of Nanofluid in Cylindrical Enclosure Filled with Porous Media

A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.

Natural Convection of MHD over a Vertical Wavy Surface in Presence of Porous Media

This paper shows the natural convective heat transfer in porous media over the vertical wavy surface and it assumes that the fluid is viscous and in-compressible. This model shows the effects of the inverse of Darcy number. The dimensional partial differential equations are converted into a dimensionless form. The non-linear system of equations is obtained and these equations are solved numerically by the finite difference method. The results are obtained for inverse Darcy number, magnetic parameter, Prandtl number, amplitude of surface, parameter of heat generation and parameter of thermal conductivity, and their effects on the velocity, temperature of the fluid and Nusselt number.

MHD natural convection with Joule and viscous heating effects in iso-flux porous medium-filled enclosures

In this study, the magnetohydrodynamics （MHD） natural convection heat transfer with Joule and viscous heating effects inside an iso-flux porous medium-filled inclined rectangular enclosure is studied numerically. An iso-heat flux is applied for heating and cooling the two opposing walls of the enclosure while the other walls are adiabatic. The Forchheimer extension of Darcy-Oberbeck-Boussinesq and energy equations is transformed into a dimensionless form using a set of suitable variables instead of a finite difference scheme. The governing parameters are the magnetic influence number, the modified Rayleigh number, the inclination angle, and the aspect ratio of the enclosure. The results show that viscous and Joule heating effects decrease heat transfer rates.

Stability of Natural Convection of Power-law Fluid and non-Darcy Flow in Porous Media

In the present work the effect of the power law exponent of power-law fluid and non-Darcy number of non-Darcy flow on stability of natural convection in porous media are studied. The computation analysis of effect of powerlaw exponent of power-law fluid and non-Darcy number of non-Darcy flow in the rectangular duct on the transition Rayleigh number Ra, which means the convective model transiting from stationary state to periodic solution. The duct has filled a porous medium saturated with the power-law non-Newtonian fluid or Newtonian fluid for non-Darcy now, in which there is uniform internal heat generation per unit volume q. In thes paper the relationship between the transition Rayleigh number Ra* and the power-law exponent n, Ra* and non-Darcy number Be, are shown .To these two aspects, the transition route from steady to chaotic convection is also obtained.

Numerical Study of 2-D Natural Convection in a Square Porous Cavity: Effect of Three Mode Heating

The work we present in this paper is a continuation of a series of studies on the numerical study of natural convection in a square porous cavity saturated by a Newtonian fluid. The left vertical wall is subjected to a temperature varying sinusoidally in time while the right vertical wall is either at a constant temperature, or varying sinusoidally in time. The upper and lower horizontal walls are thermally adiabatic. Darcy model is used, it is also assumed the fluid studied is incompressible and obeys the Boussinesq approximation. The focus is on the effect of the modulation frequency (10≤ ω≤100) on the structure of the flow and transfer thermal. The results show that the extremal stream functions (Ψmax et Ψmin), the average Nusselt number at the hot (Th) and cold (Tc) walls respectively Nuh and Nuc are periodic in the range of parameters considered in this study. In comparison with the constant heating conditions, it is found that the variable heating causes the appearance of secondary flow, whose amplification depends on the frequency of modulation of the imposed temperature but also of the heating mode. The results are shown in terms of streamlines and isotherms during a flow cycle.

Numerical Study of Natural Convection in a Porous Square Enclosure with Sinusoidally Varying Temperature Profile on the Bottom Wall

This current study focuses on the simulation of natural convection in square cavity filled with a porous medium considered homogenous, isotropic and saturated by a Newtonian fluid obeying the law of Darcy and the hypothesis of Boussinesq. The lower horizontal wall of the enclosure is subjected to a temperature varying sinusoidally with the space while the upper horizontal wall is maintained adiabatic. The vertical walls are kept cold isotherm. In order to generalize the results, all governing equations are put into dimensionless form, discretized by the Finite Difference Method and solved by the relaxed Gauss Seidel (SUR) Algorithm. A code has been proposed in Fortran 95, in order to solve numerically the equations of the problem. The study parameters are the Rayleigh-Darcy number (Ra) and the amplitude (Ar) of the hot wall temperature. The effects of the Rayleigh-Darcy number and amplitude on the dynamic and thermal field, the horizontal velocity distribution and the mean horizontal temperature distribution (y = 0.5) were presented and discussed. It emerges from this study that the increases of the amplitude and Rayleigh-Darcy number intensify the flow and the global transfer of heat in our physical domain.

On the combined heat transfer of natural convection, radiation and conduction in the non-gray semitransparent thermal fibrous insulation

A detailed numerical modeling is performed to investigate heat transfer in high-porous, high-temperature non-gray semitransparent silica insulation materials. Radiation between fibers, conduction within fibers and convection from the fibers to the surrounding fluid are considered. Macroscopic (porous media) modeling is used to determine the velocity, pressure and temperatures fields for fibrous insulation with a random packing geometry under natural convection. Based on a non-gray application of the solution to the radiative transfer equation, the value of the refractive index(n,m)is used to generate macroscopic average radiative properties such as extinction coefficient, scattering albedo and phase function. Key features of the macroscopic model include two-dimensional effects,non-gray radiative exchange, and the relaxation of the local thermodynamic non-equilibrium. The effectiveness of this numerical model is validated by the previous experimental data.

Natural Convection of Temperature-Sensitive Magnetic Fluids in Porous Media

In this article,natural convection of a temperature-sensitive magnetic fluid in a porous media is studied numerically by using lattice Boltzmann method.Results show that the heat transfer decreases when the ball numbers increase.When the magnetic field is increased,the heat transfer is enhanced;however the average wall Nusselt number increases at small ball numbers but decreases at large ball numbers due to the induced flow being more likely confined near the bottom walls with a high number of obstacles.

EFFECTS OF TRANSVERSE OSCILLATIONS ON NATURAL CONVECTIVE FLOW INDUCED BY COMBINED THERMAL AND MASS DIFFUSIONS IN POROUS MEDIA

This paper studies the unsteady heat and mass natural convection in a highly porous medium bounded by an infinite vertical porous wall. The unsteady source of the problem arises from the transverse oscillations in suction velocity of fluids, The analytical results for the problem are obtained based on the method of small parameter, and show that the natural circulation in the porous medium is affected by this kind of oscillation.

Natural Convection through Air Filter Media for Cooling of Remote Radio Heads

Passive cooling techniques are cost effective and reliable methods of cooling remote radio heads (RRH). This paper investigates the plausibility of a passive cooling technique involving exchanging warm air, from the internal cavity of RRHs, with fresh ambient air, to reduce the operating temperature using natural convection across air filters. The results indicate that, an internal air filter tube structure, with width of the enclosure, running vertically up the middle of an RRH, along with 4 pleat filter sides (2.0 ± 0.5 cm separation) provides the most effective outdoor suitable setup out of those examined. This provides a reduction in temperature of 3.9°K ± 0.4°K in the PA and 4.0°K ± 0.4°K in the radio, and a reduction in mass of 0.45 ± 0.05 kg, and is capable of withstanding water ingress and corrosive conditions including wind driven rain and salt fog.

THE NATURAL CONVECTION OF AQUIFERS WITH CONSTANT HEAT SOURCES AND ITS INFLUENCE ON TEMPERATURE FIELDS

By combining sand tank tests with numerical simulations, this paper studies the temperature fields around constant heat sources to reveal the mechanism of the natural convection and its influence on the temperature fields in the process of energy storage. Using the ＂24-channel temperature auto acquisition system＂ developed by our research group in the tests, the temperatures are recorded at measuring points within the research area in the tests, the revised Brinkman equation and a transfer-convection balance model are used for solving the aquifer water-thermal coupling problems, and through comparison of the test results with the calcula- tion results, it is discovered that the influence ranges and the variations of the two temperature fields are consistent, which validates the mathematical model. On the basis of this, we also study the influences of the heat source positions and the boundary conditions on the temperature fields, and the results show that, under the natural convection, the heat source positions may influence the distri- bution of the temperature fields, thus affect the energy storage. For the same energy storage layer, the temperature field for the top energy storage is characterized by a smaller heat influence range and a relatively concentrated temperature distribution. However, when the heat source is at the bottom, the range of a temperature field, and the temperature is relatively dispersed, which is not favorable to heat recycle, with the same heat source position, the boundary conditions determine the size of the critical Rayleigh number, and thus have an influence on the occurrence and the strength of the natural convection, and accordingly, on the temperature fields.

Non－Darcian and Anisotropic Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

Natural convection heat transfer in a horizontal enclosure filled with anisotropic porous media,being isothermally heated at bettom and cooled at top while the vertical walls being adiabatic, is numerically studied by applying the Brinkman model-a modified form of Darcy model giving consideration to the viscous effect. The results show that:(1)a larger permeability ratio (K*) causes a lower flow intensity in the enclosure and a smaller Nusselt number, all Nusselt numbers approach unity in the limit of K* → ∞;a larger thermal conductivity ratio (λ*) causes a stranger distortion of isotherms in the enclosure and a higher flow velocity near the walls, all the Nusselt numbers approach unity in the limit of λ*→0; the permeability and thermal conductivity ratios generally have opposing effects on the Nusselt number. (2) an increasing Darcy number decreases the flow intensity and heat transfer rates,which is more significant at a lower permeability ratio. In particular, with K*0.25, the Nusselt number for Da=10-3 would differ from that of Darcy flow up to an amount of 30%, an analysis neglecting the non-Darican effect will inevitably be of considerable error.

Influence of Hartmann Number on Convective Flow of Maxwell Fluid between Two Hot Parallel Plates through Porous Medium Subject to Arbitrary Shear Stress at the Boundary

Natural convection flow of unsteady Maxwell fluid with the effects of constant magnetic force in the course of a porous media is investigated in this research work. Fluid motion between a channel of parallel plates is tempted by time dependent shear stress applied on one plate. The governing partial differential equations of a model under consideration are transformed into ordinary differential equations by Laplace transform method and then solved for temperature and velocity fields. The obtained results for temperature fields are expressed in terms of complementary error function. The influences of involved parameters likes Hartmann number, Grashf number, Prandlt number and porosity parameter, on temperature and velocity profiles are shown graphically. There is no such result regarding Maxwell fluid in the existing literature.

Natural Convection Heat Transfer in a Porous Cavity with Sinusoidal Temperature Distribution Using Cu/Water Nanofluid: Double MRT Lattice Boltzmann Method

In this study,natural convection flow in a porous cavity with sinusoidal temperature distribution has been analyzed by a new double multi relaxation time(MRT)Lattice Boltzmann method(LBM).We consider a copper/water nanofluid filling a porous cavity.For simulating the temperature and flow fields,D2Q5 and D2Q9 lattices are utilized respectively,and the effects of different Darcy numbers(Da)(0.001-0.1)and various Rayleigh numbers(Ra)(10^(3)-10^(5))for porosity(ε)between 0.4 and 0.9 have been considered.Phase deviation(θ)changed from 0 toπand the volume fraction of nanoparticles(∅)varied from 0 to 6%.The present results show a good agreement with the previous works,thus confirming the reliability the new numerical method proposed in this paper.It is indicated that the heat transfer rate increases at increasing Darcy number,porosity,Rayleigh number,the volume fraction of nanoparticles and phase deviation.However,the most sensitive parameter is the Rayleigh number.The maximum Nusselt deviation is 10%,32%and 33%for Ra=10^(3),10^(4) and 10^(5),respectively,withε=0.4 toε=0.9.It can be concluded that the effect of Darcy number on the heat transfer rate increases at increasing Rayleigh number,yielding a maximum enhancement of the average Nusselt number around 12%and 61%for Ra=10^(3) and Ra=10^(5),respectively.

涡量—流函数法模拟不同高宽比和角度的腔内自然对流

采用涡量—流函数方程,对FLUENT软件进行二次开发,对重力作用下封闭空腔内的二维自然对流换热流场、温度场进行了数值模拟。对非正方形的矩形空腔内的自然对流换热进行了数值计算,结果表明不同的高宽比例对自然对流换热有很大的影响;该文还对Ra=104时放置不同角度的封闭腔进行了数值计算,揭示了重力作用下不同角度时的自然对流换热变化,发现在某一倾斜角度时(θ=45°左右),平均换热系数Numean存在极大值。

封闭腔内自然对流数值方法研究

在文献 [1]的基础上 ,将非定常流函数涡量方程的数值求解方法推广至非等距网格剖分 ,其中流函数一阶导数即速度项采用二阶精度公式 ,包含温度在内的离散方程组采用ADI迭代方法求得定常解 ,以封闭腔内自然对流为例 ,进行了不同瑞利数 (Ra)条件下数值试验 ,对Ra =10 6的计算进行了必要的处理 .计算结果表明 ,该数值方法推导简单 ,计算稳定 ,为采用K -ε模式计算封闭腔内层流到湍流的转捩打下基础 .

多孔介质内自然对流传热传质研究

该文研究了含内热源圆柱形多孔介质内不均匀温度分布产生的浮力效应引起的自然对流。给出了以流函数表示的无量纲基本方程，用控制容积法对方程离散并进行了数值计算，得到了多孔介质内的流场、温度场和浓度场，讨论了瑞利数Ｒａ和刘易斯数Ｌｅ对多孔介质传热传质的影响。

封闭方腔内自然对流问题的高精度紧致差分格式

提出数值求解二维非定常不可压涡量-流函数Navier-Stokes/Boussinesq方程组的高精度紧致差分格式,格式空间为四阶精度,时间为二阶精度,并且是无条件稳定的.为了验证高精度紧致差分格式的精确性和可靠性,对有解析解的二维非定常不可压Navier-Stokes/Boussinesq方程组的Dirichlet问题和典型的封闭方腔自然对流问题进行数值模拟.